On a Family of 2-Variable Orthogonal Krawtchouk Polynomials
We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the 9−j symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146521 |
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| Cite this: | On a Family of 2-Variable Orthogonal Krawtchouk Polynomials / F.A. Grünbaum, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146521 |
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Grünbaum, F.A. Rahman, M. 2019-02-09T19:49:29Z 2019-02-09T19:49:29Z 2010 On a Family of 2-Variable Orthogonal Krawtchouk Polynomials / F.A. Grünbaum, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45 DOI:10.3842/SIGMA.2010.090 https://nasplib.isofts.kiev.ua/handle/123456789/146521 We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the 9−j symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel corresponding to a ''poker dice'' type probability model. The proof in this paper derives and makes use of the necessary and sufficient conditions of orthogonality in establishing orthogonality as well as indicating their geometrical significance. We also derive a 5-term recurrence relation satisfied by these polynomials. We thank one referee in particular for a very methodical job that has rendered this into a more accurate paper. In an area where several people have made important contributions he has helped us tell the story properly. The research of the first author was supported in part by the Applied Math. Sciences subprogram of the Of fice of Energy Research, USDOE, under Contract DE-AC03-76SF00098, and by AFOSR under contract FA9550-08-1-0169. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Family of 2-Variable Orthogonal Krawtchouk Polynomials Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
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| title |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials |
| spellingShingle |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials Grünbaum, F.A. Rahman, M. |
| title_short |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials |
| title_full |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials |
| title_fullStr |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials |
| title_full_unstemmed |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials |
| title_sort |
on a family of 2-variable orthogonal krawtchouk polynomials |
| author |
Grünbaum, F.A. Rahman, M. |
| author_facet |
Grünbaum, F.A. Rahman, M. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the 9−j symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel corresponding to a ''poker dice'' type probability model. The proof in this paper derives and makes use of the necessary and sufficient conditions of orthogonality in establishing orthogonality as well as indicating their geometrical significance. We also derive a 5-term recurrence relation satisfied by these polynomials.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146521 |
| citation_txt |
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials / F.A. Grünbaum, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 19 назв. — англ. |
| work_keys_str_mv |
AT grunbaumfa onafamilyof2variableorthogonalkrawtchoukpolynomials AT rahmanm onafamilyof2variableorthogonalkrawtchoukpolynomials |
| first_indexed |
2025-12-07T17:33:44Z |
| last_indexed |
2025-12-07T17:33:44Z |
| _version_ |
1850871721884647424 |